MathDB

Princeton has an endowment of

5

million dollars and wants to invest it into improving campus life. The university has three options: it can either invest in improving the dorms, campus parties or dining hall food quality. If they invest

a

million dollars in the dorms, the students will spend an additional

5a

hours per week studying. If the university invests

b

million dollars in better food, the students will spend an additional

3b

hours per week studying. Finally, if the

c

million dollars are invested in parties, students will be more relaxed and spend

11c - c^2

more hours per week studying. The university wants to invest its

5

million dollars so that the students get as many additional hours of studying as possible. What is the maximal amount that students get to study?

Problem Statement